Differentiation Questions and Answers

Factor the trinomial 16c 22c 3 Select the correct choice below

Benjamin s Backpacks can sell backpack a Write the cost and revenue equations b Graph both equations for 0 to 50 bac c Use the graph to estimate the number d Write the profit formula

1 If f x 8 sin x find f x Find f 0 8

For the function y f x x 4x 1 x 2 find 3 df 1 dy y 3

For the function y f x 4x 6 3 a Find df dx f 8 768 b Find a formula for x y f y c Find at x 8 3 Vy 6 4 df 1 dy at y f 8 f 8 1 192 X

Let f x 4x 5 5 7x 6 5 15 14 40x 4x 5 7x 6 15 210x 4x 5 7x 6 4 2

et TEL V Prove that if U is T invariant then UO is T invariant

35 36 Find an equation of the tangent line to the given curve at the specified point 35 y 2x x 1 1 1 36 y e cos x 0 1

39 40 Find f x and x 39 f x x e

If f x sin x find f x Find f 3

If f x 3x 3 find f x 2 Find f 5

Fill in the blank The equation y mx b the The equation y mx b th

What is the value of x if gx 1 2 25 x 1 2 2 7 O 0 x WON 5 x 4

An equation for the depreciation of a car is given by y A 1 r where y current value of the car A original cos rate of depreciation and t time in years The value of a car is half what it originally cost The rate of depreciation 10 Approximately how old is the car O 3 3 years 5 0 years O 5 6 years 066 years

19 If sec 0 0 and tan 0 then in which quadrant does 0 lie C or III B II E IV C III

Fill in the blank An illustration of all points whose coordin An illustration of all points whose coordin

Select the correct choice

Graph the solution set of the inequality whe

Use logarithmic differentiation to determine the derivative value If f x 8x x find 4 f 4

1 Evaluate the following integrals a 3 2x 1 2 S x 2x e dx 0 use tabulaltion

Find the derivative of the function e g x 26x

Find the derivative of the function f x below f x ln 13 e 9

A company has found that the number of items sold X depends upon the price P at which they re sold according the equation x 18200 3p The price has been increasing by 2 per month Find the rate at which revenue is changing when the price is 40 Note the answer might be negative dollars per month

Find x rounded to one decimal place X 55 60 X 65

Find the side labeled x X 25 60

Find the derivative of the function g x F g x 1x 3x 2 e

Find the exponential function f x ax whose grap f x y 4 3 2

5 4 3 N 7 3 4 What is the least possible degree of the polynomial graphed above

For what value of k will the polynomial P x x 7x kx 3 have the same remainder when it is divided by x 1 and by x 4 k

A person standing close to the edge on top of a 80 foot building throws a ball vertically upward The quadratic function h t 16t 64t 80 models the ball s height about the ground h t in feet t seconds after it was thrown a What is the maximum height of the ball feet b How many seconds does it take until the ball hits the ground seconds

The demand equation for a certain product is given by P 130 0 06x where p is the unit price in dollars of the product and x is the number of units produced The total revenue obtained by producing and selling x units is given by R xp Determine prices p that would yield a revenue of 8330 dollars Lowest such price Highest such price

solution D 6D 9 y e

Let P t 35 1 e kt 57 represent the expecte score for a student who studies t hours for a test Suppose k 0 19 and test scores must be integers What is the highest score the student can expect 93 X If the student does not study what score can he expect 57

Analyze the graph of the function F x x 216 X a What is the domain of F x OA x x 0 x 6 and x 6 B xlx 0 and x 6 C x x 0 D All real numbers b What is the equation of the vertical asymptote s of F x Select the correct choice below and fill in any answer boxes within your choice OA x Use a comma to separate answers as needed Type an integer or a fract B There is no vertical asymptote

1 Find all maxima and minima including at endpoints of f x x 120 2x on the horizontal span of 0 to 60 Enter the maximum and minimum values of f not the value of x at those points max min 2 ind the minimum value of the function f x 4 5x 2x 3 If f x x 5x 2 evaluate the following f 2 4 R Determine whether the given function has a maximum value or a minimum value and then find the value f x x 40x 4 The function has a maximum value when x The value of f x at this point is

ans L Let P t 35 1 e kt 57 represent the expected score for a student who studies t hours for a test Suppose k 0 19 and test scores must be integers What is the highest score the student can expect If the student does not study what score can he expect

Solve for n in the equation below using logarithms Round answer to 3 decimal places 2 10 9 49

sin COS tan X 1 2 0 3 1 ans Find the solution of the exponential equation 18e 1517

If log 6x 3 3 then x Note Round your answer to 2 decimal places

Write the equation in logarithmic form ew y

ans Solve for z in the equation below It may be helpful to convert the equation into exponential form Write answer as an integer or reduced fraction 5 log7 z 4 19

Solve for x log5 x log5 x 4 1 X Round your final answer to 6 decimal places Note Do not round until the final step

This question has several parts that must be complete Tutorial Exercise Find the absolute extrema of the function on the y 4 cos x 0 2 Step 1 The absolute extrema of a function on a closed in Begin by differentiating the function with respect

0 21 0 41 Points DETAILS PREVIOUS ANSWERS A lawn sprinkler is constructed in such a way that de dt v sin 20 X 32 where the constant v is the speed of the water 45 0 135 8 105 8 135 is constant where 8 ranges bet 8 75 8 45 LARCALC12 3 32

A polynomial of degree 4 P x has leading coefficient 1 and has roots of 3 i and 1 with multiplicity 2 Find a possible formula for P x You do not need to simplify your answer P x x 1 x x 3 i x x 3 i X Answer format should look like x a 2 x b i x b i

Mr Ewald decides to make and sell Left Handed Smoke Shifters as a side business The function below gives the average cost in dollars per Smoke Shifter when x Smoke Shifters are produced A x 4x 250 x Use the function to answer the following questions Determine A 13 and complete the sentence explaining the meaning of your answer Round your answer to the nearest cent The average cost to produce 13 Left Handed Smoke Shifters is How many Smoke Shifters must be produced in order to reduce the average cost to 9 each To reduce the average cost to produce each Smoke Shifter down to 9 Smoke Shifters must be produced Give the equation of the horizontal asymptote of A x Horizontal Asymptote Select a sentence to explain its significance in this situation

Given 1i is a root of polynomial P x x 5x x 5 find the remaining roots and write factored form Find a possible formula for P x You do not need to simplify your answer P x Answer format should look like x a x bi x bi

Find all zeros of f x x 9x 21x 5 Enter the zeros separated by commas Enter exact value not decimal approximations To receive credit for this question the following steps must be presented in the solution Step 1 List all potential rational zeros of the function using Rational Zero Theorem Step 2 Use the remainder theorem to determine whether the potential rational zeros are roots of the function If the remainder is 0 the candidate is a zero If the remainder is not 0 discard the candidate Step 3 Divide the polynomial function by the root obtained in the step 2 using synthetic division or long division A quotient will be drived at this step Step 4 If the quotient is a quadratic go to the step 5 If the quotient is not a quadratic repeat the steps 2 3 until the quotient is a quadratic Step 5 Use the quotient to find the remaining zeros by factoring or the quadratic formula

For what value of k will the polynomial P x x 2x kx 7 have the same remainder when it is divided by x 4 and by x 1 k

ints 1 22 3 20 125 and has a horizontal asymptote at y 20